I once owned a Trillium 13 with "bathroom," but they are much fewer and farther between than the one with the couch/bunks in front.
The unloaded weight
on mine was listed as 1095#, but I believe that didn't count the refrigerator
I would think you could tow with vehicle that had a 2000# limit, but you'd want to watch what you were carrying (added stuff brings the weight
up, plus I think the 1095# might have been a bit optimistic anyway). You'd probably want to consider brakes
for the trailer.
Also, check your owner's manual. Some cars require you to subtract the weight
of the occupants and cargo from the towing weight (just something to check).
If an automatic, you'd probably want a transmission cooler. I'm not "current" on Camry's, but when I was station wagon shopping a number of years ago, the transmission was one of the possible worry items on that generation of Camry (late 80s, so maybe not applicable).
Overall the 13-foot trailers with bathroom are fairly rare, I'd say.